The U.S. Pat. Ser. No. 09/037,088 now U.S. Pat. No. 6,027,069, and Ser. No. 09/161,457 now U.S. Pat. No. 6,019,308, disclose a device for dispensing a roll of adhesive tape. These two devices are intended to overcome the deficiencies of a device which is disclosed in the U.S. Pat. No. 4,659,031 and is provided with a revolving member 41 of a tubular construction, and a grip member 42 having a tubular body 43, as shown in FIG. 1. The revolving member 41 is pivoted with the tubular body 43 of the grip member 42. If the revolving member 41 and the tubular body 43 are not pivoted with a proper tightness, the adhesive tape roll is prone to sway at the time when it is held with hand to facilitate the dispensing of the tape. In the event that the revolving member 41 and the tubular body 43 are pivoted with an excessive tightness, the revolving member 41 which is forced into a spool 44 tends to refrain the tubular body 43 of the grip member 42, thereby resulting in a sluggish rotation of the revolving member 41.